Can the backup software mail alerts via email?

Yes, BackupChain offers several means to alert  you to backup task statuses and problems. These include: sending email alerts directly via SMTP (see Log Options tab of your task), monitoring the Windows Event Viewer logs because BackupChain will write to it automatically, and lastly, you have the option of running external scripts, commands, or applications when a task starts, fails, ends, and for other phases of the backup task execution.

Also see How to Customize HTML Email Alerts for Backup Tasks, and the User Guide.

Please note that using free email providers, such as Google, or Outlook, may not work as these platforms now use strict spam filters that make their email service unsuitable for automated email alerts. Please use your organization’s email server instead or a compatible general purpose SMTP server. If none are available, please note that we offer a free SMTP service running in the BackupChain Cloud to customers who use the Server Enterprise or Platinum editions.

You would also run PowerShell or batch files when a task starts, fails, ends successfully, etc. using your own alert mechanism or scripts. This may be another workaround if SMTP or the internet is not available in your infrastructure.